The development of morals, like every other kind of human development, involves BOTH nature AND nurture. Maybe one can be so strong as to completely dominate the other, but that's probably pretty rare.
As far as the nature aspect, humans are extremely unlikely to "evolve" a lower level of morality and here's why:
Humans, by nature, are social creatures. A bunch of hermits can survive by themselves, but they will have fewer offspring than their social counterparts. Thus, humans who retain their social tendencies will drive evolution of the species.
Immoral actions may provide benefits for the actor which will increase resources and the likelihood of more offspring along with it. However, immorality will always be frowned upon by the community by its very nature. The more immoral the actions, the more likely the community is to ostracize the offender thereby decreasing social interaction and likelihood of more offspring.
At some point, ostracism will always trump resources making the immoral less likely to reproduce overall. This is because even a rich man cannot reproduce alone. However, until that point, the immoral will be about as likely to reproduce as the moral because of the relative balance of resources and social condemnation. Thus, from an evolutionary standpoint, the level of morality is unlikely to significantly change.
Its significantly more likely that the relative standards of immorality will shift in ways that cause older and younger generations to feud within cultures, while entire cultures feud with each other as globalization increases their interactions.